a gas mixtuer consists of equal masses of methane(molecular weight 16.0) and argon (atomic weight 40.0) if the partial pressure of argon is 26.6 kPa, what is that of methane in the same units?
10.7
26.7
66.7
34.1
I am going with 26.7
Do you agree and why please
Thanks Andy
You wouldn't think pressure Ar = pressure CH4 because equal masses ( although true) contain different number of moles.
Here is what I would do.
Select a convenient number for grams, say 50 g.
Convert 50 g to moles CH4.
Convert 50 g to moles Ar.
Now find mole fraction Ar.
mole fraction Ar = moles Ar/total moles.
PAr = XAr*Ptotal
Solve for Ptotal. (PAr = 26.6
Then PAr + PCH4 = Ptotal
Solve for PCH4
ok so P ch4 = 13.67 kPa
where do i go from there??
No it isn't.
moles CH4 = 50/16 = 3.125
moles Ar = 50/40 = 1.25
total moles = 3.125 + 1.25 = 4.375
XAr = 1.25/4.375 = 0.286
XAr*Ptotal = PAr
0.286*Ptotal = 26.6
Ptotal = 26.6/0.286 = 93
Then 93 = PCH4 + PAr
PCH4 = 93.0 - 26.6 = ??
Answer is in kPa. Where do you go from here. You're here.
so its a trick question as the unwary would say that CH4 and Ar under ideal behavior would be the same and the answer would be 26.7....??
But its obviously worded to catch out the unwary about partial pressure questions?
Finally i can rest and the answer is 66.7 NOT 26.7!!!!!
andy
To determine the partial pressure of methane in the gas mixture, we can use the concept of mole fraction. The mole fraction of a component in a gas mixture is equal to the ratio of the number of moles of that component to the total number of moles in the mixture.
In this case, since the mass of methane and argon in the mixture is equal, we can assume that they have equal moles. Let's consider the total number of moles as "x."
Since methane has a molecular weight of 16.0 g/mol, the number of moles of methane will be (16.0 g/mol) * x.
Similarly, since argon has an atomic weight of 40.0 g/mol, the number of moles of argon will be (40.0 g/mol) * x.
Now, since the partial pressure of argon is given as 26.6 kPa, we know that the mole fraction of argon (X argon) is equal to the partial pressure of argon divided by the total pressure (P total):
X argon = (partial pressure of argon) / (total pressure)
X argon = 26.6 kPa / (partial pressure of argon + partial pressure of methane)
Since the total pressure is the sum of the partial pressures, we can rewrite the equation as:
X argon = 26.6 kPa / (26.6 kPa + partial pressure of methane)
Since the mole fraction of argon and methane sum up to 1, we can also express the mole fraction of methane (X methane) as:
X methane = 1 - X argon
Now, we can substitute the mole fraction of argon in the equation to find the partial pressure of methane:
X methane = 1 - (26.6 kPa / (26.6 kPa + partial pressure of methane))
Simplifying this equation will give us the value of the partial pressure of methane.
Let's calculate it:
X methane = 1 - (26.6 kPa / (26.6 kPa + partial pressure of methane))
X methane = partial pressure of methane / (26.6 kPa + partial pressure of methane)
Now, we can set this equation equal to the mole fraction of methane (which we assume is equal to the mole fraction of argon):
partial pressure of methane / (26.6 kPa + partial pressure of methane) = partial pressure of methane / total pressure
Simplifying further, we get:
partial pressure of methane = (26.6 kPa + partial pressure of methane) * partial pressure of methane / total pressure
Now, we have the equation in terms of the partial pressure of methane. We can substitute the given value of the total pressure to find the partial pressure of methane.
Given that total pressure is not mentioned in the question, we cannot determine the actual value of the partial pressure of methane. So, we cannot confirm if 26.7 kPa is the correct answer.